The main ideas of the Declaration of Independence have to do with what makes government legitimate and what government is supposed to do.
In the Declaration, Jefferson tells us what gives a government the right to rule over its people. He says that governments have the right to rule their people because the people give their consent to be ruled. This can be seen where he writes that
... Governments are instituted among Men, deriving their just powers from the consent of the governed...
Jefferson also tells us what the purpose of government is. Its purpose, he says, is to protect the rights that we all have by virtue of having been born human. He says that
... all men are created equal, that they are endowed by their Creator with certain inalienable Rights, that among these are Life, Liberty and the pursuit of Happiness...
The whole purpose of government, he says, is "to secure these rights."
This first part of the Declaration is the most important part. There, Jefferson puts forward the main ideas of the document, the ideas that will be the basis of American democracy in years to come.